biography
pronunciation:
[oyler]
| sex:
| male
|
| lived:
| (1707–83)
|
| biography:
| Mathematician, born in Basel, N Switzerland. He studied mathematics there under Jean Bernoulli, and became professor of physics (1731) and then of mathematics (1733) at the St Petersburg Academy of Sciences. In 1738 he lost the sight of one eye. In 1741 he moved to Berlin as director of mathematics and physics in the Berlin Academy, but returned to St Petersburg in 1766, soon afterwards losing the sight of his other eye. He was a giant figure in 18th-c mathematics, publishing over 800 different books and papers, on every aspect of pure and applied mathematics, physics and astronomy. His Introductio in analysin infinitorum (1748) and later treatises on differential and integral calculus and algebra remained standard textbooks for a century and his notations, such as e and π have been used ever since. For the princess of Anhalt-Dessau he wrote Lettres à une princesse d'Allemagne (1768–72), giving a clear non-technical outline of the main physical theories of the time. He had a prodigious memory, which enabled him to continue mathematical work and to compute complex calculations in his head when he was totally blind. He is without equal in the use of algorithms to solve problems. Several important notions in mathematics are named after him. Euler's constant (usually denoted by γ) is the limit, as n→∞, of 1 + ½ + ⅓ + ¼...1/n − logen, approximately 0·577. Euler's function (denoted by &phis; (n)) refers to the number of integers in the set 1,2,3,...n − 1 which are prime to n; thus &phis; (9) = 6, since 6 of the integers 1,2,3,...8 are prime to 9. Euler's formula for polyhedra states that if a polyhedron has v vertices, f faces, and e edges, v + f − e = 2 for all polyhedra; thus a cube has 8 vertices, 12 edges, and 6 faces, and 8 + 6 − 12 = 2. In any triangle, the centre O of the circumcircle, the orthocentre H, and the centroid G lie on a straight line, called the Euler Line, and OG : GH = 1 : 2. |
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